Comment: forthcoming, The RAND Journal of EconomicsWe propose an empirical framework for asymmetric Cournot oligopoly with private information about variable costs. First, considering a linear demand for a homogenous product with a random intercept, we characterize the Bayesian Cournot-Nash equilibrium. Then we establish the identification of the joint distribution of demand and firm-specific cost distributions. Following the identification steps, we propose a likelihood-based estimation method and apply it to the global market for crude-oil and quantify the welfare effect of private information. We also consider extensions of the model to include either product differentiation, conduct parameters, nonlinear demand, or selective entry.